Blow-up analysis for an elliptic equation describing stationary vortex flows with variable intensities in 2D-turbulence
Blow-up analysis for an elliptic equation describing stationary vortex flows with variable intensities in 2D-turbulence
复制标题
DOI：
10.1016/j.jde.2010.06.006
复制
发表时间：
2010-09
影响因子：
2.4
通讯作者：
H. Ohtsuka;T. Ricciardi;Takashi Suzuki
中科院分区：
文献类型：
--
作者：
H. Ohtsuka;T. Ricciardi;Takashi Suzuki
当环流数密度受到概率测度时，我们考虑在具有一般环流约束的点涡旋的高能标度极限中产生的平均场方程。从数学上讲，这样的方程是一个非局部椭圆方程，包含取决于此概率度量的指数非线性。我们分析了与循环数相关的解的爆炸序列的行为。作为我们分析的应用，我们推导了相关变分泛函的改进 Trudinger-Moser 不等式。
We consider the mean field equation arising in the high-energy scaling limit of point vortices with a general circulation constraint, when the circulation number density is subject to a probability measure. Mathematically, such an equation is a non-local elliptic equation containing an exponential nonlinearity which depends on this probability measure. We analyze the behavior of blow-up sequences of solutions in relation to the circulation numbers. As an application of our analysis we derive an improved Trudinger–Moser inequality for the associated variational functional.